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A340073
a(n) = (x-1) / gcd(x-1, phi(x)), where x = A003961(n), i.e., n with its prime factorization shifted one step towards larger primes.
4
0, 1, 1, 4, 1, 7, 1, 13, 6, 5, 1, 11, 1, 8, 17, 40, 1, 37, 1, 31, 27, 19, 1, 67, 8, 25, 31, 49, 1, 13, 1, 121, 4, 14, 19, 28, 1, 17, 21, 47, 1, 41, 1, 29, 29, 43, 1, 101, 12, 73, 47, 19, 1, 187, 5, 74, 57, 23, 1, 157, 1, 55, 137, 364, 59, 97, 1, 85, 9, 23, 1, 337, 1, 61, 61, 103, 71, 127, 1, 283, 156, 32, 1, 247, 11
OFFSET
1,4
COMMENTS
Prime shifted analog of A160596.
FORMULA
a(n) = A160596(A003961(n)).
a(n) = A253885(n-1) / A340071(n) = (A003961(n)-1) / A340071(n).
PROG
(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A340073(n) = { my(x=A003961(n)); (x-1)/gcd(x-1, eulerphi(x)); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 28 2020
STATUS
approved